Question

WebLearn Mathematics and Statistics for Manufacturing Engineers (MATH2185 1910) Student Test Page Fourier series andDF Question the discrete Founer transtorm is detined as: Fk-Lje k0,1,2. ..,N-1 1=0 The following nine data values are measured at evenly spaced time intervals: -0.011, 0.688, 0.983, 0.717, -0.001, -0.687, -0.952, -0.701, 0.01 For this test data, calculate the real and imaginary parts of F. Maintain at least eight decimal digit accuracy throughout all your calculations. When entering your final answers you may round your estimate to five decimal digit accuracy. For example 1.673526755 or 1.67353 See the following example from MatLab. Uses the fft() command to find the discrete Fourier transform of a set of data values y [0.5146, 0.9485,1.2788, 1.4762,1.5028, 1.3101,0.8358] ; Yafft (y) fnt-etrcat (I'd,. disp (eprintf ('\nk for ic-l:length (Y) dispisprintf (fmt, ic-1, real (Y (ic)), imag (Y (ic))) ) i -14.10f',+i(,'-14.10f,) 1) F(k) '); end F (k) 7.8668000000 -1.6329778499 +i (-0.0460558570) -0.3575862848 +1 (-0.1442516542) -0.1417358652 +i (-0.0474369403) +1 (0.0000000000 1 2 -0.1417358652 +1 (0.0474369403 -0.3575862848 +1 (0.1442516542 -1.6329778499 +1(0.0460558570 4 Re(F1) Im(F1) Skipped Skipped O Submit...O Check Syntax.. O Previous... O Test Menu... University-Discdaimer 1 About Privacy

format compact

format long

clear

y=[-0.003, 0.197, 0.3, 0.402, 0.496, 0.603, 0.7, 0.797, 0.996, 1.02];

Y=fft(y);

%% Display F[k]

fmt=strcat(['%d',' ','%-14.10f','+i(','%-14.10f',')']);

disp(sprintf('\nk F[k]'));

for ic=1:length(Y)

disp(sprintf(fmt,ic-1,real(Y(ic)),imag(Y(ic))));

end

%%

Answer 1

format compact format long clear y[-0.011, 0.688, 0.983, 0.717, -0.001, -0.687, -0.952, -0.701, 0.01 1 Y-fft(y) Display F[ k] fmt-strcat ([ '$d',' ', ' %-14.10f','+i(','%-14.10f',')']); disp (sprintf (' \nk F[k]')); for ic-1:1ength(Y) disp (sprintf ( fmt,ic-1,real (Y ( ic)), imag (Y (ic)))); end 응용웅용용 응용 용웅웅을 음용 응을 End of Code 응응용용용용용용응용용용응용용 k FIk 0 0.0460000000 1 1.3366763305 +i (0.0000000000 +i (-3.7742484 727) +i (0.64268 71 21 3 2 -0.5643254679 3 -0.3920000000 +i (0.2771281292 4 -0.4528508626 +i (0.080 74 63 9 72 5 -0.4528508626 ti (-0.08074639 72 6 -0.3920000000 ti(-0.2771281292) 7 -0.5643254 679 +i (-0.6426871213 ) +i (3.7742484 727 8 1.3366763305 Published with MATLAB R2018a 1

format compact
format long
clear

y=[-0.011, 0.688, 0.983, 0.717, -0.001, -0.687, -0.952, -0.701, 0.01];
Y=fft(y);

%%Display F[k]
fmt=strcat(['%d',' ','%-14.10f','+i(','%-14.10f',')']);
disp(sprintf('\nk F[k]'));

for ic=1:length(Y)

    disp(sprintf(fmt,ic-1,real(Y(ic)),imag(Y(ic))));

end

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